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The Variational Problem and Background Field in the Renormalization Group Method for Non-Linear Sigma Models

Abhishek Goswami

Abstract

We study the variational problem as described by Balaban in his renormalization group method for Yang-Mills theories in $d= 3, 4$ and adapt it to a class of Non-Linear Sigma Models in $d=2$. The result of the variational problem is a minimal configuration which can serve as a classical background field in the renormalization group analysis.

The Variational Problem and Background Field in the Renormalization Group Method for Non-Linear Sigma Models

Abstract

We study the variational problem as described by Balaban in his renormalization group method for Yang-Mills theories in and adapt it to a class of Non-Linear Sigma Models in . The result of the variational problem is a minimal configuration which can serve as a classical background field in the renormalization group analysis.
Paper Structure (21 sections, 107 equations)

This paper contains 21 sections, 107 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Steepest descent
  4. Block averaging
  5. Spaces of regular configurations
  6. Symmetry subgroup
  7. New space
  8. Variational problem statement
  9. RG transformation
  10. Defining the variational problem
  11. Proof
  12. Minimizers
  13. Mapping transformation
  14. Proof of Proposition 4
  15. Linearizing transformation
  16. ...and 6 more sections